On the Jarzynski relation for dissipative quantum dynamics

In this note, we will discuss how to compactly express the Jarzynski identity for an open quantum system with dissipative dynamics. In quantum dynamics we must avoid explicitly measuring the work directly, which is tantamount to continuously monitoring the state of the system, and instead measure the heat ?ow from the environment. These measurements can be concisely represented with Hermitian map superoperators, which provide a convenient and compact representations of correlation functions and sequential measurements of quantum systems